Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturban...Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control (AFTC) algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno (T-S) fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator (ELS), and the comparative experimental results indicate that AFTC controller is effective for PTSS.展开更多
This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM meth...This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.展开更多
This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information o...This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.展开更多
In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lya...In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.展开更多
In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality ...In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.展开更多
This paper is dedicated to the study of adaptive input-to-state stable synchronization of uncertain time-delay Lur’e systems with exterior interference. With the help of the Lyapunov function approach, a sufficient c...This paper is dedicated to the study of adaptive input-to-state stable synchronization of uncertain time-delay Lur’e systems with exterior interference. With the help of the Lyapunov function approach, a sufficient condition for the input-to-state stability of the synchronization-error system is derived, which is theoretically less conservative than a previously reported criterion in the absence of parameter uncertainties. On the basis of the present condition, a co-design of the feedback gain and estimates of the uncertain parameters is given to determine the desired adaptive synchronization controller. Finally, an example with simulations is provided to demonstrate the applicability and superiority of the analysis and design strategies.展开更多
This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We s...This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS.For the case of linear networked systems,a complete characterisation of the stability condition is provided,together with two distributed algorithms for computing the network gain:the classical Jacobi iterations and a message-passing algorithm.For the case of nonlinear networked systems,characterisation of the ISS condition can be done using M-functions,and Jacobi iterations can be used to compute the network gain.展开更多
We develop tools for the investigation of input-to-state practical stability(ISpS)and integral input-to-state practical stability(iISpS)of non-autonomous infinite-dimensional systems in Banach spaces.Sufficient condit...We develop tools for the investigation of input-to-state practical stability(ISpS)and integral input-to-state practical stability(iISpS)of non-autonomous infinite-dimensional systems in Banach spaces.Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions.The practical stability analysis is accomplished with the help of scalar practical stable functions.Then,a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces.We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t.inputs from Lp-spaces.Furthermore,we illustrate the theory with an example of a semi-linear reaction-diffusion equation.展开更多
For any p∈[1,+∞]and any r∈[p,+∞],by using the approximative Lyapunov method,the L^(r)-integral input-to-state stability(L^(r)-iISS)in the spatial L^(p-norm for a class of 1-D nonlinear parabolic PDEs with distribu...For any p∈[1,+∞]and any r∈[p,+∞],by using the approximative Lyapunov method,the L^(r)-integral input-to-state stability(L^(r)-iISS)in the spatial L^(p-norm for a class of 1-D nonlinear parabolic PDEs with distributed in-domain disturbances and under homogeneous Robin boundary conditions is assessed.Furthermore,when p∈[1,+∞),under additional assumptions on the relationship between the coefficients of the equation and the parameter p,the W^(1,p)-iISS in the spatial W^(1,p)-norm for the consider system is proved.In addition,in the special case of p∈[2,+∞),a refined𝐿L^(r)-iISS estimate in the spatial W^(1,p)-norm is established for the considered system.展开更多
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stoch...In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.展开更多
Compared with input-to-state stability(ISS)in global version,the concept of local input-to-state stability(LISS)is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating th...Compared with input-to-state stability(ISS)in global version,the concept of local input-to-state stability(LISS)is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI)methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.展开更多
In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switchin...In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.展开更多
The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation o...The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.展开更多
This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertai...This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.展开更多
In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems （PWA） with time delays are considered. Both feedback with time delays and feedback without time d...In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems （PWA） with time delays are considered. Both feedback with time delays and feedback without time delays are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are展开更多
In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one ...In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one always prefers to construct the strict Lyapunov functionals to analyse stability of time-delay systems.However,it may be not an easy task to do this for some timedelay systems.This paper proposes an input-to-state stability theorem based on a time-scale uniformly asymptotically stable function.The advantage of this theorem is that it is dependent on the non-strict Lyapunov functional,whose time-scale derivative can be non-negative on some time intervals.Then,some approaches are established to construct the strict Lyapunov functionals based on the non-strict ones.It is shown that input-to-state stability theorems can be also formulated in terms of these strict Lyapunov functionals.Finally,to illustrate the effectiveness of the main results,an example is given.展开更多
This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction(FCDR)systems governed by coupled time fractional partial differential equations(TFPDEs)under matched a...This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction(FCDR)systems governed by coupled time fractional partial differential equations(TFPDEs)under matched and unmatched disturbances over actuator/sensor networks using output feedback,fractional sliding mode(FSM)algorithm and sampled-in-space sensing.Here it is assumed that sensors provide discrete in space measurements,i.e.,spatially averaged measurements(SAMs),and a limited number of sensors are allocated in a spatial domain.A sampled-data observation problem is first in investigation,which contains to design an FSM observer against boundary disturbances and to prove input-to-state stability(ISS)of the proposed observer.Using this observer and backstepping approach,the authors develop an output feedback FSM controller and establish the reaching condition to FSM surface.Using the fractional Lyapunov method,ISS of the closed-loop dynamics is achieved.Theoretical results are verified by numerical simulations.展开更多
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic...This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.展开更多
Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview o...Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview of recent developments on the control of linear and nonlinear systems when the control input is subject to quantization or the quantized states or outputs are used as feedback measurements. The co-existence of high-dimeasionality, quantization, nonlinearity and uncertainty poses great challenges to quantized control of nonlinear systems and thus calls for new ideas and techniques. The field of quantized nonlinear control is still at its infancy. Preliminary results in our recent work based on input-to-state stability and cyclic-small-gain theorems are reviewed. The open problems in quantized nonlinear control are also outlined.展开更多
The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order ...The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.展开更多
基金National High-tech Research and Development Program of China (2009AA04Z412)"111" ProjectBUAA Fund of Graduate Education and Development
文摘Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control (AFTC) algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno (T-S) fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator (ELS), and the comparative experimental results indicate that AFTC controller is effective for PTSS.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission(XK100080537)
文摘This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.
基金This work was supported by the National Natural Science Foundation of China(62173215)Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04,ZR2020ZD24)the Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions(2019KJI008).
文摘This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.
基金supported by National Natural Science Foundation of China (No. 60874006)Natural Science Foundation of Hei-longjiang Province for Youth (No. QC2009C99)
文摘In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.
文摘In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.
基金the Natural Science Foundation of the Anhui Higher Education Institutions(Grant No.KJ2020A0248)the National Natural Science Foundation of China(Grant Nos.61806004 and 61503002)the Open Project of Anhui Province Key Laboratory of Special and Heavy Load Robot(Grant No.TZJQR005-2020)。
文摘This paper is dedicated to the study of adaptive input-to-state stable synchronization of uncertain time-delay Lur’e systems with exterior interference. With the help of the Lyapunov function approach, a sufficient condition for the input-to-state stability of the synchronization-error system is derived, which is theoretically less conservative than a previously reported criterion in the absence of parameter uncertainties. On the basis of the present condition, a co-design of the feedback gain and estimates of the uncertain parameters is given to determine the desired adaptive synchronization controller. Finally, an example with simulations is provided to demonstrate the applicability and superiority of the analysis and design strategies.
基金supported in part by the National Natural Science Foundation of China(Nos.U21A20476,U1911401,U22A20221,62273100,62073090).
文摘This paper studies the stability problem for networked control systems.A general result,called network gain theorem,is introduced to determine the input-to-state stability(ISS)for interconnected nonlinear systems.We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS.For the case of linear networked systems,a complete characterisation of the stability condition is provided,together with two distributed algorithms for computing the network gain:the classical Jacobi iterations and a message-passing algorithm.For the case of nonlinear networked systems,characterisation of the ISS condition can be done using M-functions,and Jacobi iterations can be used to compute the network gain.
文摘We develop tools for the investigation of input-to-state practical stability(ISpS)and integral input-to-state practical stability(iISpS)of non-autonomous infinite-dimensional systems in Banach spaces.Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions.The practical stability analysis is accomplished with the help of scalar practical stable functions.Then,a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces.We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t.inputs from Lp-spaces.Furthermore,we illustrate the theory with an example of a semi-linear reaction-diffusion equation.
基金supported in part by the National Natural Science Foundation of China under grant number 11901482the Natural Sciences and Engineering Research Council of Canada under grant RGPIN-2018-04571.
文摘For any p∈[1,+∞]and any r∈[p,+∞],by using the approximative Lyapunov method,the L^(r)-integral input-to-state stability(L^(r)-iISS)in the spatial L^(p-norm for a class of 1-D nonlinear parabolic PDEs with distributed in-domain disturbances and under homogeneous Robin boundary conditions is assessed.Furthermore,when p∈[1,+∞),under additional assumptions on the relationship between the coefficients of the equation and the parameter p,the W^(1,p)-iISS in the spatial W^(1,p)-norm for the consider system is proved.In addition,in the special case of p∈[2,+∞),a refined𝐿L^(r)-iISS estimate in the spatial W^(1,p)-norm is established for the considered system.
基金the National Natural Science Foundation of China (No.60221301, No.60428304).
文摘In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.
基金supported by the National Natural Science Foundation of China(Grant Nos 50977047 and 50907038)
文摘Compared with input-to-state stability(ISS)in global version,the concept of local input-to-state stability(LISS)is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI)methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61773235,61273123,61374004,61403227part by Program for New Century Excellent Talents in University under Grant No.NCET-13-0878part by the Taishan Scholar Project of Shandong Province of China under Grant No.tsqn20161033
文摘In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.
基金the National Natural Science Foundation of China (Grant No. 60674038)
文摘The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.
基金supported by the National Natural Science Foundation of China under Grant No.61977042the Foundation for Innovative Research Groups of National Natural Science Foundation of China under Grant No.61821004。
文摘This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China under Grant No.60874006Natural Science Foundation of Heilong jiang Province for Youth under Grant No.QC2009C99
文摘In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems （PWA） with time delays are considered. Both feedback with time delays and feedback without time delays are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are
基金This work was supported by the National Natural Science Foundation of China[61873150]the China Postdoctoral Science Foundation[2020M672110].
文摘In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one always prefers to construct the strict Lyapunov functionals to analyse stability of time-delay systems.However,it may be not an easy task to do this for some timedelay systems.This paper proposes an input-to-state stability theorem based on a time-scale uniformly asymptotically stable function.The advantage of this theorem is that it is dependent on the non-strict Lyapunov functional,whose time-scale derivative can be non-negative on some time intervals.Then,some approaches are established to construct the strict Lyapunov functionals based on the non-strict ones.It is shown that input-to-state stability theorems can be also formulated in terms of these strict Lyapunov functionals.Finally,to illustrate the effectiveness of the main results,an example is given.
基金supported by the National Natural Science Foundation of China under Grant Nos.62203070,12161141013,and 62173348Jiangsu Government Scholarship for Overseas Stuides under Grant No.SCZ2307400004+1 种基金Jiangsu Innovation Program for Graduates under Grant No.KYCX233068the Science and Technology Project of Changzhou University under Grant No.KYP2402263C。
文摘This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction(FCDR)systems governed by coupled time fractional partial differential equations(TFPDEs)under matched and unmatched disturbances over actuator/sensor networks using output feedback,fractional sliding mode(FSM)algorithm and sampled-in-space sensing.Here it is assumed that sensors provide discrete in space measurements,i.e.,spatially averaged measurements(SAMs),and a limited number of sensors are allocated in a spatial domain.A sampled-data observation problem is first in investigation,which contains to design an FSM observer against boundary disturbances and to prove input-to-state stability(ISS)of the proposed observer.Using this observer and backstepping approach,the authors develop an output feedback FSM controller and establish the reaching condition to FSM surface.Using the fractional Lyapunov method,ISS of the closed-loop dynamics is achieved.Theoretical results are verified by numerical simulations.
基金supported by National Natural Science Foundation of China (No. 60774010, 10971256, and 60974028)Jiangsu"Six Top Talents" (No. 07-A-020)+2 种基金Natural Science Foundation of Jiangsu Province (No. BK2009083)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.07KJB510114)Natural Science Foundation of Xuzhou Normal University (No. 08XLB20)
文摘This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
基金Supported by National Science Foundation of USA （DMS-0906659. ECCS-1230040）
文摘Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview of recent developments on the control of linear and nonlinear systems when the control input is subject to quantization or the quantized states or outputs are used as feedback measurements. The co-existence of high-dimeasionality, quantization, nonlinearity and uncertainty poses great challenges to quantized control of nonlinear systems and thus calls for new ideas and techniques. The field of quantized nonlinear control is still at its infancy. Preliminary results in our recent work based on input-to-state stability and cyclic-small-gain theorems are reviewed. The open problems in quantized nonlinear control are also outlined.
基金supported by National Natural Science Foundation of China(No.60974127)Natural Science Foundation of Shandong Province of China(No.ZR2011FM033)
文摘The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.
